Is it possible to create a 'logic system' equivalent to humans?
There is of course a vast amount of work in the area of Automatic Theorem Proving, but most of it is simply concerned with proof, rather than human notions of beauty, elegance, parsimony etc.

There has however been some work in this general area over the years:


Douglas Lenat's famous AM ('Amateur Mathematician').
Douglas Hofstadter's NUMBO program for number sequence extrapolation.
A range of publications by Simon Colton
Shalosh B. Ekhad, the automated proof assistant for Artificial Combinatorics created by Doron Zeilberg and credited by him as a co-author on numerous papers.